Apparatus for encoding a speech signal employing acelp in the autocorrelation domain

ABSTRACT

An apparatus for encoding a speech signal by determining a codebook vector of a speech coding algorithm is provided. The apparatus includes a matrix determiner for determining an autocorrelation matrix R, and a codebook vector determiner for determining the codebook vector depending on the autocorrelation matrix R. The matrix determiner is configured to determine the autocorrelation matrix R by determining vector coefficients of a vector r, wherein the autocorrelation matrix R includes a plurality of rows and a plurality of columns, wherein the vector r indicates one of the columns or one of the rows of the autocorrelation matrix R, wherein R(i, j)=r(|i−j|), wherein R(i, j) indicates the coefficients of the autocorrelation matrix R, wherein i is a first index indicating one of a plurality of rows of the autocorrelation matrix R, and wherein j is a second index indicating one of the plurality of columns of the autocorrelation matrix R.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of copending InternationalApplication No. PCT/EP2013/066074, filed Jul. 31, 2013, which isincorporated herein by reference in its entirety, and additionallyclaims priority from U.S. Application No. 61/710,137, filed Oct. 5,2012, which is also incorporated herein by reference in its entirety.

BACKGROUND OF THE INVENTION

The present invention relates to audio signal coding, and, inparticular, to an apparatus for encoding a speech signal employing ACELPin the autocorrelation domain.

In speech coding by Code-Excited Linear Prediction (CELP), the spectralenvelope (or equivalently, short-time time-structure) of the speechsignal is described by a linear predictive (LP) model and the predictionresidual is modelled by a long-time predictor (LTP, also known as theadaptive codebook) and a residual signal represented by a codebook (alsoknown as the fixed codebook). The latter, the fixed codebook, isgenerally applied as an algebraic codebook, where the codebook isrepresented by an algebraic formula or algorithm, whereby there is noneed to store the whole codebook, but only the algorithm, whilesimultaneously allowing for a fast search algorithm. CELP codecsapplying an algebraic codebook for the residual are known as AlgebraicCode-Excited Linear Prediction (ACELP) codecs (see [1], [2], [3], 4]).

In speech coding, employing an algebraic residual codebook is theapproach of choice in main stream codecs such as [17], [13], [18]. ACELPis based on modeling the spectral envelope by a linear predictive (LP)filter, the fundamental frequency of voiced sounds by a long timepredictor (LTP) and the prediction residual by an algebraic codebook.The LTP and algebraic codebook parameters are optimized by a leastsquares algorithm in a perceptual domain, where the perceptual domain isspecified by a filter.

The computationally most complex part of ACELP-type algorithms, thebottleneck, is optimization of the residual codebook. The only currentlyknown optimal algorithm would be an exhaustive search of a size N^(p)space for every sub-frame, where at every point, an evaluation of O(N²)complexity may be performed. Since typical values are sub-frame lengthN=64 (i.e. 5 ms) with p=8 pulses, this implies more than 10²⁰ operationsper second. Clearly this is not a viable option. To stay within thecomplexity limits set by hardware requirements, codebook optimizationapproaches have to operate with non-optimal iterative algorithms. Manysuch algorithms and improvements to the optimization process have beenpresented in the past, for example [17], [19], [20], [21], [22].

Explicitly, the ACELP optimisation is based on describing the speechsignal x(n) as the output of a linear predictive model such that theestimated speech signal is

{circumflex over (x)}(n)=−Σ_(k=1) ^(m) a(k){circumflex over(x)}(n−k)+{circumflex over (e)}(k)  (1)

where a(k) are the LP coefficients and ê(k) is the residual signal. Invector form, this equation can be expressed as

{circumflex over (x)}=Hê  (2)

where matrix H is defined as the lower triangular Toeplitz convolutionmatrix with diagonal h(0) and lower diagonals h(1), . . . , h(39) andthe vector h(k) is the impulse response of the LP model. It should benoted that in this notation the perceptual model (which usuallycorresponds to a weighted LP model) is omitted, but it is assumed thatthe perceptual model is included in the impulse response h(k). Thisomission has no impact on the generality of results, but simplifiesnotation. The inclusion of the perceptual model is applied as in [1].

The fitness of the model is measured by the squared error. That is,

ϵ²=Σ_(k=1) ^(N)(x(k)−{circumflex over (x)}(k))²=(e−ê)^(H) H ^(H)H(e−ê).  (3)

This squared error is used to find the optimal model parameters. Here,it is assumed that the LTP and the pulse codebook are both used to modelthe vector e. The practical application can be found in the relevantpublications (see [1-4]).

In practice, the above measure of fitness can be simplified as follows.Let the matrix B=H^(T)H comprise the correlations of h(n), let c_(k) bethe k′th fixed codebook vector and set ê=g c_(k) , where g is a gainfactor. By assuming that g is chosen optimally, then the codebook issearched by maximizing the search criterion

$\begin{matrix}{\frac{C_{k}^{2}}{E_{k}} = {\frac{\left( {x^{T}\; {Hc}_{k}} \right)^{2}}{c_{k}^{T}{Bc}_{k}} = \frac{\left( {d^{T}c_{k}} \right)^{2}}{c_{k}^{T}{Bc}_{k}}}} & (4)\end{matrix}$

where d=H^(T)x is a vector comprising the correlation between the targetvector and the impulse response h(n) and superscript T denotestranspose. The vector d and the matrix B are computed before thecodebook search. This formula is commonly used in optimization of boththe LTP and the pulse codebook.

Plenty of research has been invested in optimising the usage of theabove formula. For example,

-   1) Only those elements of matrix B are calculated that are actually    accessed by the search algorithm. Or:-   2) The trial-and-error algorithm of the pulse search is reduced to    trying only such codebook vectors which have a high probability of    success, based on prior screening (see for example [1,5]).

A practical detail of the ACELP algorithm is related to the concept ofzero impulse response (ZIR). The concept appears when considering theoriginal domain synthesis signal in comparison to the synthesisedresidual. The residual is encoded in blocks corresponding to the frameor sub-frame size. However, when synthesising the original domain signalwith the LP model of Equation 1, the fixed length residual will have aninfinite length “tail”, corresponding to the impulse response of the LPfilter. That is, although the residual codebook vector is of finitelength, it will have an effect on the synthesis signal far beyond thecurrent frame or sub-frame. The effect of a frame into the future can becalculated by extending the codebook vector with zeros and calculatingthe synthesis output of Equation 1 for this extended signal. Thisextension of the synthesised signal is known as the zero impulseresponse. Then, to take into account the effect of prior frames inencoding the current frame, the ZIR of the prior frame is subtractedfrom the target of the current frame. In encoding the current frame,thus, only that part of the signal is considered, which was not alreadymodelled by the previous frame.

In practice, the ZIR is taken into account as follows: When a (sub)frameN−1 has been encoded, the quantized residual is extended with zeros tothe length of the next (sub)frame N. The extended quantized residual isfiltered by the LP to obtain the ZIR of the quantized signal. The ZIR ofthe quantized signal is then subtracted from the original (notquantized) signal and this modified signal forms the target signal whenencoding (sub)frame N. This way, all quantization errors made in(sub)frame N−1 will be taken into account when quantizing (sub)frame N.This practice improves the perceptual quality of the output signalconsiderably.

However, it would be highly appreciated if further improved concepts foraudio coding would be provided.

SUMMARY

According to an embodiment, an apparatus for encoding a speech signal bydetermining a codebook vector of a speech coding algorithm may have: amatrix determiner for determining an autocorrelation matrix R, and acodebook vector determiner for determining the codebook vector dependingon the autocorrelation matrix R, wherein the matrix determiner isconfigured to determine the autocorrelation matrix R by determiningvector coefficients of a vector r, wherein the autocorrelation matrix Rincludes a plurality of rows and a plurality of columns, wherein thevector r indicates one of the columns or one of the rows of theautocorrelation matrix R, wherein R(i, j)=r(|i−j|), wherein R(i, j)indicates the coefficients of the autocorrelation matrix R, wherein i isa first index indicating one of a plurality of rows of theautocorrelation matrix R, and wherein j is a second index indicating oneof the plurality of columns of the autocorrelation matrix R.

According to another embodiment, a method for encoding a speech signalby determining a codebook vector of a speech coding algorithm may havethe steps of: determining an autocorrelation matrix R, and determiningthe codebook vector depending on the autocorrelation matrix R, whereindetermining an autocorrelation matrix R includes determining vectorcoefficients of a vector r, wherein the autocorrelation matrix Rincludes a plurality of rows and a plurality of columns, wherein thevector r indicates one of the columns or one of the rows of theautocorrelation matrix R, wherein R(i, j)=r(|i−j|), wherein R(i, j)indicates the coefficients of the autocorrelation matrix R, wherein i isa first index indicating one of a plurality of rows of theautocorrelation matrix R, and wherein j is a second index indicating oneof the plurality of columns of the autocorrelation matrix R.

According to another embodiment, a decoder for decoding an encodedspeech signal being encoded by an apparatus for encoding a speech signalby determining a codebook vector of a speech coding algorithm, whichapparatus may have:

-   -   a matrix determiner for determining an autocorrelation matrix R,        and    -   a codebook vector determiner for determining the codebook vector        depending on the autocorrelation matrix R,    -   wherein the matrix determiner is configured to determine the        autocorrelation matrix R by determining vector coefficients of a        vector r, wherein the autocorrelation matrix R includes a        plurality of rows and a plurality of columns, wherein the vector        r indicates one of the columns or one of the rows of the        autocorrelation matrix R, wherein

R(i,j)=r(|i−j|),

-   -   wherein R(i, j) indicates the coefficients of the        autocorrelation matrix R, wherein i is a first index indicating        one of a plurality of rows of the autocorrelation matrix R, and        wherein j is a second index indicating one of the plurality of        columns of the autocorrelation matrix R    -   to acquire a decoded speech signal.

According to another embodiment, a method for decoding an encoded speechsignal being encoded according to the method for encoding a speechsignal by determining a codebook vector of a speech coding algorithm,which method for encoding may have the steps of:

-   -   determining an autocorrelation matrix R, and    -   determining the codebook vector depending on the autocorrelation        matrix R,    -   wherein determining an autocorrelation matrix R includes        determining vector coefficients of a vector r, wherein the        autocorrelation matrix R includes a plurality of rows and a        plurality of columns, wherein the vector r indicates one of the        columns or one of the rows of the autocorrelation matrix R,        wherein

R(i,j)=r(|i−j|),

-   -   wherein R(i, j) indicates the coefficients of the        autocorrelation matrix R, wherein i is a first index indicating        one of a plurality of rows of the autocorrelation matrix R, and        wherein j is a second index indicating one of the plurality of        columns of the autocorrelation matrix R    -   to acquire a decoded speech signal.

According to another embodiment, a system may have:

-   -   an apparatus for encoding a speech signal by determining a        codebook vector of a speech coding algorithm, which apparatus        may have:        -   a matrix determiner for determining an autocorrelation            matrix R, and        -   a codebook vector determiner for determining the codebook            vector depending on the autocorrelation matrix R,            -   wherein the matrix determiner is configured to determine                the autocorrelation matrix R by determining vector                coefficients of a vector r, wherein the autocorrelation                matrix R includes a plurality of rows and a plurality of                columns, wherein the vector r indicates one of the                columns or one of the rows of the autocorrelation matrix                R, wherein

R(i,j)=r(|i−j|),

-   -   -   -   wherein R(i, j) indicates the coefficients of the                autocorrelation matrix R, wherein i is a first index                indicating one of a plurality of rows of the                autocorrelation matrix R, and wherein j is a second                index indicating one of the plurality of columns of the                autocorrelation matrix R,

    -   for encoding an input speech signal to acquire an encoded speech        signal, and

    -   a decoder for decoding an encoded speech signal being encoded by        an apparatus for encoding a speech signal by determining a        codebook vector of a speech coding algorithm, which apparatus        may have:        -   a matrix determiner for determining an autocorrelation            matrix R, and        -   a codebook vector determiner for determining the codebook            vector depending on the autocorrelation matrix R,        -   wherein the matrix determiner is configured to determine the            autocorrelation matrix R by determining vector coefficients            of a vector r, wherein the autocorrelation matrix R includes            a plurality of rows and a plurality of columns, wherein the            vector r indicates one of the columns or one of the rows of            the autocorrelation matrix R, wherein

R(i,j)=r(|i−j|),

-   -   -   wherein R(i, j) indicates the coefficients of the            autocorrelation matrix R, wherein i is a first index            indicating one of a plurality of rows of the autocorrelation            matrix R, and wherein j is a second index indicating one of            the plurality of columns of the autocorrelation matrix R

    -   to acquire a decoded speech signal,

    -   for decoding the encoded speech signal to acquire a decoded        speech signal.

According to another embodiment, a method may have the steps of:

-   -   encoding an input speech signal according to the method for        encoding a speech signal by determining a codebook vector of a        speech coding algorithm, which method for encoding may have the        steps of:        -   determining an autocorrelation matrix R, and        -   determining the codebook vector depending on the            autocorrelation matrix R,        -   wherein determining an autocorrelation matrix R includes            determining vector coefficients of a vector r, wherein the            autocorrelation matrix R includes a plurality of rows and a            plurality of columns, wherein the vector r indicates one of            the columns or one of the rows of the autocorrelation matrix            R, wherein

R(i,j)=r(|i−j|),

-   -   -   wherein R(i, j) indicates the coefficients of the            autocorrelation matrix R, wherein i is a first index            indicating one of a plurality of rows of the autocorrelation            matrix R, and wherein j is a second index indicating one of            the plurality of columns of the autocorrelation matrix R,

    -   to acquire an encoded speech signal, and

    -   decoding the encoded speech signal according to the method for        decoding an encoded speech signal being encoded according to the        method for encoding a speech signal by determining a codebook        vector of a speech coding algorithm, which method for encoding        may have the steps of:        -   determining an autocorrelation matrix R, and        -   determining the codebook vector depending on the            autocorrelation matrix R,        -   wherein determining an autocorrelation matrix R includes            determining vector coefficients of a vector r, wherein the            autocorrelation matrix R includes a plurality of rows and a            plurality of columns, wherein the vector r indicates one of            the columns or one of the rows of the autocorrelation matrix            R, wherein

R(i,j)=r(|i−j|),

-   -   -   wherein R(i, j) indicates the coefficients of the            autocorrelation matrix R, wherein i is a first index            indicating one of a plurality of rows of the autocorrelation            matrix R, and wherein j is a second index indicating one of            the plurality of columns of the autocorrelation matrix R, to            acquire a decoded speech signal,

    -   to acquire a decoded speech signal.

Another embodiment may have a computer program for implementing, whenbeing executed on a computer or signal processor, the method forencoding a speech signal by determining a codebook vector of a speechcoding algorithm, which method may have the steps of:

-   -   determining an autocorrelation matrix R, and    -   determining the codebook vector depending on the autocorrelation        matrix R,    -   wherein determining an autocorrelation matrix R includes        determining vector coefficients of a vector r, wherein the        autocorrelation matrix R includes a plurality of rows and a        plurality of columns, wherein the vector r indicates one of the        columns or one of the rows of the autocorrelation matrix R,        wherein

R(i,j)=r(|i−j|),

-   -   wherein R(i, j) indicates the coefficients of the        autocorrelation matrix R, wherein i is a first index indicating        one of a plurality of rows of the autocorrelation matrix R, and        wherein j is a second index indicating one of the plurality of        columns of the autocorrelation matrix R.

Another embodiment may have a computer program for implementing, whenbeing executed on a computer or signal processor, the method fordecoding an encoded speech signal being encoded according to the methodfor encoding a speech signal by determining a codebook vector of aspeech coding algorithm, which method for encoding may have the stepsof:

-   -   determining an autocorrelation matrix R, and    -   determining the codebook vector depending on the autocorrelation        matrix R,    -   wherein determining an autocorrelation matrix R includes        determining vector coefficients of a vector r, wherein the        autocorrelation matrix R includes a plurality of rows and a        plurality of columns, wherein the vector r indicates one of the        columns or one of the rows of the autocorrelation matrix R,        wherein

R(i,j)=r(|i−j|),

-   -   wherein R(i, j) indicates the coefficients of the        autocorrelation matrix R, wherein i is a first index indicating        one of a plurality of rows of the autocorrelation matrix R, and        wherein j is a second index indicating one of the plurality of        columns of the autocorrelation matrix R,    -   to acquire a decoded speech signal.

Another embodiment may have a computer program for implementing, whenbeing executed on a computer or signal processor, the method which mayhave the steps of:

-   -   encoding an input speech signal according to the method for        encoding a speech signal by determining a codebook vector of a        speech coding algorithm, which method for encoding may have the        steps of:        -   determining an autocorrelation matrix R, and        -   determining the codebook vector depending on the            autocorrelation matrix R,            -   wherein determining an autocorrelation matrix R includes                determining vector coefficients of a vector r, wherein                the autocorrelation matrix R includes a plurality of                rows and a plurality of columns, wherein the vector r                indicates one of the columns or one of the rows of the                autocorrelation matrix R, wherein

R(i,j)=r(|i−j|),

-   -   -   wherein R(i, j) indicates the coefficients of the            autocorrelation matrix R, wherein i is a first index            indicating one of a plurality of rows of the autocorrelation            matrix R, and wherein j is a second index indicating one of            the plurality of columns of the autocorrelation matrix R, to            acquire an encoded speech signal, and

    -   decoding the encoded speech signal according to the method for        decoding an encoded speech signal being encoded according to the        method for encoding a speech signal by determining a codebook        vector of a speech coding algorithm, which method for encoding        may have the steps of:        -   determining an autocorrelation matrix R, and        -   determining the codebook vector depending on the            autocorrelation matrix R,        -   wherein determining an autocorrelation matrix R includes            determining vector coefficients of a vector r, wherein the            autocorrelation matrix R includes a plurality of rows and a            plurality of columns, wherein the vector r indicates one of            the columns or one of the rows of the autocorrelation matrix            R, wherein

R(i,j)=r(|i−j|),

-   -   -   wherein R(i, j) indicates the coefficients of the            autocorrelation matrix R, wherein i is a first index            indicating one of a plurality of rows of the autocorrelation            matrix R, and wherein j is a second index indicating one of            the plurality of columns of the autocorrelation matrix R, to            acquire a decoded speech signal, to acquire a decoded speech            signal.

The apparatus is configured to use the codebook vector to encode thespeech signal. For example, the apparatus may generate the encodedspeech signal such that the encoded speech signal comprises a pluralityof Linear Prediction coefficients, an indication of the fundamentalfrequency of voiced sounds (e.g., pitch parameters), and an indicationof the codebook vector, e.g, an index of the codebook vector.

Moreover, a decoder for decoding an encoded speech signal being encodedby an apparatus according to the above-described embodiment to obtain adecoded speech signal is provided.

Furthermore a system is provided. The system comprises an apparatusaccording to the above-described embodiment for encoding an input speechsignal to obtain an encoded speech signal. Moreover, the systemcomprises a decoder according to the above-described embodiment fordecoding the encoded speech signal to obtain a decoded speech signal.

Improved concepts for the objective function of the speech codingalgorithm ACELP are provided, which take into account not only theeffect of the impulse response of the previous frame to the currentframe, but also the effect of the impulse response of the current frameinto the next frame, when optimizing parameters of current frame. Someembodiments realize these improvements by changing the correlationmatrix, which is central to conventional ACELP optimisation to anautocorrelation matrix, which has Hermitian Toeplitz structure. Byemploying this structure, it is possible to make ACELP optimisation moreefficient in terms of both computational complexity as well as memoryrequirements. Concurrently, also the perceptual model applied becomesmore consistent and interframe dependencies can be avoided to improveperformance under the influence of packet-loss.

Speech coding with the ACELP paradigm is based on a least squaresalgorithm in a perceptual domain, where the perceptual domain isspecified by a filter. According to embodiments, the computationalcomplexity of the conventional definition of the least squares problemcan be reduced by taking into account the impact of the zero impulseresponse into the next frame. The provided modifications introduce aToeplitz structure to a correlation matrix appearing in the objectivefunction, which simplifies the structure and reduces computations. Theproposed concepts reduce computational complexity up to 17% withoutreducing perceptual quality.

Embodiments are based on the finding that by a slight modification ofthe objective function, complexity in the optimization of the residualcodebook can be further reduced. This reduction in complexity comeswithout reduction in perceptual quality. As an alternative, since ACELPresidual optimization is based on iterative search algorithms, with thepresented modification, it is possible to increase the number ofiterations without an increase in complexity, and in this way obtain animproved perceptual quality.

Both the conventional as well as the modified objective functions modelperception and strive to minimize perceptual distortion. However, theoptimal solution to the conventional approach is not necessarily optimalwith respect to the modified objective function and vice versa. Thisalone does not mean that one approach would be better than the other,but analytic arguments do show that the modified objective function ismore consistent. Specifically, in contrast to the conventional objectivefunction, the provided concepts treat all samples within a sub-frameequally, with consistent and well-defined perceptual and signal models.

In embodiments, the proposed modifications can be applied such that theyonly change the optimization of the residual codebook. It does thereforenot change the bit-stream structure and can be applied in a back-wardcompatible manner to existing ACELP codecs.

Moreover, a method for encoding a speech signal by determining acodebook vector of a speech coding algorithm is provided. The methodcomprises:

-   -   Determining an autocorrelation matrix R. And:    -   Determining the codebook vector depending on the autocorrelation        matrix R.

Determining an autocorrelation matrix R comprises determining vectorcoefficients of a vector r. The autocorrelation matrix R comprises aplurality of rows and a plurality of columns. The vector r indicates oneof the columns or one of the rows of the autocorrelation matrix R,wherein

R(i,j)=r(|i−j|),

R(i, j) indicates the coefficients of the autocorrelation matrix R,wherein i is a first index indicating one of a plurality of rows of theautocorrelation matrix R, and wherein j is a second index indicating oneof the plurality of columns of the autocorrelation matrix R.

Furthermore, a method for decoding an encoded speech signal beingencoded according to the method for encoding a speech signal accordingto the above-described embodiment to obtain a decoded speech signal isprovided.

Moreover, a method is provided. The method comprises:

-   -   Encoding an input speech signal according to the above-described        method for encoding a speech signal to obtain an encoded speech        signal. And:    -   Decoding the encoded speech signal to obtain a decoded speech        signal according to the above-described method for decoding a        speech signal.

Furthermore, computer programs for implementing the above-describedmethods when being executed on a computer or signal processor areprovided.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the present invention will be detailed subsequentlyreferring to the appended drawings, in which:

FIG. 1 illustrates an apparatus for encoding a speech signal bydetermining a codebook vector of a speech coding algorithm according toan embodiment,

FIG. 2 illustrates a decoder according to an embodiment and a decoder,and

FIG. 3 illustrates a system comprising an apparatus for encoding aspeech signal according to an embodiment and a decoder.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 illustrates an apparatus for encoding a speech signal bydetermining a codebook vector of a speech coding algorithm according toan embodiment.

The apparatus comprises a matrix determiner (110) for determining anautocorrelation matrix R, and a codebook vector determiner (120) fordetermining the codebook vector depending on the autocorrelation matrixR.

The matrix determiner (110) is configured to determine theautocorrelation matrix R by determining vector coefficients of a vectorr.

The autocorrelation matrix R comprises a plurality of rows and aplurality of columns, wherein the vector r indicates one of the columnsor one of the rows of the autocorrelation matrix R, wherein R(i,j)=r(|i−j|).

R(i, j) indicates the coefficients of the autocorrelation matrix R,wherein i is a first index indicating one of a plurality of rows of theautocorrelation matrix R, and wherein j is a second index indicating oneof the plurality of columns of the autocorrelation matrix R.

The apparatus is configured to use the codebook vector to encode thespeech signal. For example, the apparatus may generate the encodedspeech signal such that the encoded speech signal comprises a pluralityof Linear Prediction coefficients, an indication of the fundamentalfrequency of voiced sounds (e.g. pitch parameters), and an indication ofthe codebook vector.

For example, according to a particular embodiment for encoding a speechsignal, the apparatus may be configured to determine a plurality oflinear predictive coefficients (a(k)) depending on the speech signal.Moreover, the apparatus is configured to determine a residual signaldepending on the plurality of linear predictive coefficients (a(k)).Furthermore, the matrix determiner 110 may be configured to determinethe autocorrelation matrix R depending on the residual signal.

In the following, some further embodiments of the present invention aredescribed.

Returning to equations 3 and 4, wherein Equation 3 defines a squarederror indicating a fitness of the perceptual model as:

ϵ²=Σ_(k=1) ^(N)(x(k)−{circumflex over (x)}(k))²=(e−ê)^(H) H ^(H)H(e−ê).  (3)

and wherein Equation 4

$\begin{matrix}{\frac{C_{k}^{2}}{E_{k}} = {\frac{\left( {x^{T}\; {Hc}_{k}} \right)^{2}}{c_{k}^{T}{Bc}_{k}} = {\frac{\left( {d^{T}c_{k}} \right)^{2}}{c_{k}^{T}{Bc}_{k}}.}}} & (4)\end{matrix}$

indicates the search criterion, which is to be maximized.

The ACELP algorithm is centred around Equation 4, which in turn is basedon Equation 3.

Embodiments are based on the finding that analysis of these equationsreveals that the quantized residual values e(k) have a very differenteffect on the error energy (depending on the index k. For example, whenconsidering the indices k=1 and k=N, if the only non-zero value of theresidual codebook would appear at k=1, then the error energy results to:

ϵ₁ ²=Σ_(k=1) ^(N)(x(k)−e(l)h(k))²  (5)

while for k=N, the error energy results to:

ϵ_(N) ²=(x(N)−e(N)h(l))²+Σ_(k=1) ^(N-1)(x(k))².  (6)

In other words, e(l) is weighted with the impulse response h(k) on therange 1 to N, while e(N) is weighted with only h(l). In terms ofspectral weighting, this means that each e(k) is weighted with adifferent spectral weighting function, such that, in the extreme, e(N)is linearly-weighted. From a perceptual modelling perspective, it wouldmake sense to apply the same perceptual weight for all samples within aframe. Equation 3 should thus be extended such that it takes intoaccount the ZIR into the next frame. It should be noticed that here,inter alia, the difference to conventional technology is that both theZIR from the previous frame and also the ZIR into the next frame aretaken into account.

Let e(k) be the original, unquantized residual and e(k) the quantisedresidual. Furthermore, let both residuals be non-zero in the range 1 toN and zero elsewhere. Then

x(n)=−Σ_(k=1) ^(m) a(k)x(n−k)+e(n)=Σ_(k=1) ^(∞) e(n−k)h(k)

{circumflex over (x)}(n)=−Σ_(k=1) ^(m) a(k){circumflex over(x)}(n−k)+ê(n)=Σ_(k=1) ^(∞) ê(n−k)h(k)  (7)

Equivalently, the same relationships in matrix form can be expressed as:

x={tilde over (H)}e

{circumflex over (x)}={tilde over (H)}ê  (8)

where {tilde over (H)} is the infinite dimensional convolution matrixcorresponding to the impulse response h(k). Inserting into Equation 3yields

ϵ² =∥{tilde over (H)}e−{tilde over (H)}ê∥ ²=(e−ê)^(T) {tilde over (H)}^(T) {tilde over (H)}(e−ê)=(e−ê)^(T) R(e−ê)  (9)

where R={tilde over (H)}^(T){tilde over (H)} is the finite size,Hermitian Toeplitz matrix corresponding to the autocorrelation of h(n).By a similar derivation as for Equation 4, the objective function isobtained:

$\begin{matrix}{\frac{\left( {e^{T}R\hat{e}} \right)^{2}}{\left( {{\hat{e}}^{T}R\hat{e}} \right)} = {\frac{\left( {d^{T}e} \right)^{2}}{\left( {{\hat{e}}^{T}R\hat{e}} \right)}.}} & (10)\end{matrix}$

This objective function is very similar to Equation 4. The maindifference is that instead of the correlation matrix B, here a HermitianToeplitz matrix R is in the denominator.

As explained above, this novel formulation has the benefit that allsamples of the residual e within a frame will receive the sameperceptual weighting. However, importantly, this formulation introducesconsiderable benefits to computational complexity and memoryrequirements as well. Since R is a Hermitian Toeplitz matrix, the firstcolumn r(0) . . . r(N−1) defines the matrix completely. In other words,instead of storing the complete N×N matrix, it is sufficient to storeonly the N×1 vector r(k), thus yielding a considerable saving in memoryallocation. Moreover, computational complexity is also reduced since itis not necessary to determine all N×N elements, but only the first Nx 1column. Also indexing within the matrix is simple, since the element(i,j) can be found by R(i,j)=r(|i−j|).

Since the objective function in Equation 10 is so similar to Equation 4,the structure of the general ACELP can be retained. Specifically, any ofthe following operations can be performed with either objectivefunction, with only minor modifications to the algorithm:

-   1. Optimisation of the LTP lag (adaptive codebook)-   2. Optimisation of the pulse codebook for modelling the residual    (fixed codebook)-   3. Optimisation of the gains of LTP and pulses, either separately or    jointly-   4. Optimisation of any other parameters whose performance can be    measured by the squared error of Equation 3.

The only part that has to be modified in conventional ACELP applicationsis the handling of the correlation matrix B, which is replaced by matrixR, as well as the target, which may include the ZIR into the followingframe.

Some embodiments employ the concepts of the present invention by,wherever in the ACELP algorithm, where the correlation matrix B appears,it is replaced by the autocorrelation matrix R. If all instances of thematrix B are omitted, then calculating its value can be avoided.

For example, the autocorrelation matrix R is determined by determiningthe coefficients of the first column r(0), . . . , r(N−1) of theautocorrelation matrix R.

The matrix R is defined in Equation 9 by R=H^(T)H, whereby its elementsR_(ij)=r(i−j) can be calculated through

$\begin{matrix}{{r(k)} = {{{h(k)}*{h\left( {- k} \right)}} = {\sum\limits_{l}^{\;}{{h(l)}{h\left( {l - k} \right)}}}}} & \left( {9a} \right)\end{matrix}$

That is, the sequence r(k) is the autocorrelation of h(k).

Often, however, r(k) can be obtained by even more effective means.Specifically, in speech coding standards such as AMR and G.718, thesequence h(k) is the impulse response of a linear predictive filter A(z)filtered by a perceptual weighting function W(z), which is taken toinclude the pre-emphasis. In other words, h(k) indicates a perceptuallyweighted impulse response of a linear predictive model.

The filter A(z) is usually estimated from the autocorrelation of thespeech signal r_(X)(k), that is, r_(X)(k) is already known. SinceH(z)=A⁻¹(u)W(z), it follows that the autocorrelation sequence r(k) canbe determined by calculating the autocorrelation of w(k) by

$\begin{matrix}{{r_{w}(k)} = {{{w(k)}*{w\left( {- k} \right)}} = {\sum\limits_{l}^{\;}{{w(l)}{w\left( {l - k} \right)}}}}} & \left( {9b} \right)\end{matrix}$

whereby the autocorrelation of h(k) is

$\begin{matrix}{{{r(k)} - {{r_{x}(k)}*{r_{w}(k)}}} = {\sum\limits_{l}^{\;}{{r_{w}(l)}{{r_{x}\left( {l - k} \right)}.}}}} & \left( {9c} \right)\end{matrix}$

Depending on the design of the overall system, these equations may, insome embodiments, be modified accordingly.

A codebook vector of a codebook may then, e.g., be determined based onthe autocorrelation matrix R. In particular, Equation 10 may, accordingto some embodiments, be used to determine a codebook vector of thecodebook.

In this context, Equation 10 defines the objective function in the form

${f\left( \hat{e} \right)} = \frac{\left( {d^{T}\hat{e}} \right)^{2}}{{\hat{e}}^{T}R\hat{e}}$

which is otherwise the same form as in the speech coding standards AMRand G.718 but such that the matrix R now has symmetric Toeplitzstructure. The objective function is basically a normalized correlationbetween the target vector d and the codebook vector and ê the bestpossible codebook vector is that, which gives the highest value for thenormalized correlation f(ê), e.g., which maximizes the normalizedcorrelation f(ê).

Codebook vectors can thus optimized with the same approaches as in thementioned standards. Specifically, for example, the very simplealgorithm for finding the best algebraic codebook (i.e. the fixedcodebook) vector ê for the residual can be applied, as described below.It should, however, be noted, that significant effort has been investedin the design of efficient search algorithms (c.f. AMR and G.718), andthis search algorithm is only an illustrative example of application.

-   1. Define an initial codebook vector ê_(p)=[0, 0 . . . 0]^(T) and    set the number of pulses to p=0.-   2. Set the initial codebook quality measure to f₀=0.-   3. Set temporary codebook quality measure to f_(p)=f_(p-1).-   4. For each position k in the codebook vector Increase p by one.    -   (ii) If position k already contains a negative pulse, continue        to step vii.    -   (iii) Create a temporary codebook vector e_(g) ⁺=ê_(p-1) and add        a positive pulse at position k.    -   (iv) Evaluate the quality of the temporary codebook vector by        f(e_(p) ⁺).    -   (v) If the temporary codebook vector is better than any of the        previous, f(ê_(p) ⁺)>f_(p), then save this codebook vector, set        f_(p)=f(ê_(p) ⁺) and continue to next iteration.    -   (vi) If position k already contains a positive pulse, continue        to next iteration.    -   (vii) Create a temporary codebook vector e_(p) ⁻=ê_(p-1) and add        a negative pulse at position k.    -   (viii) Evaluate the quality of the temporary codebook vector by        f(e_(p) ⁻).    -   (ix) If the temporary codebook vector is better than any of the        previous, f(ê_(p) ⁻)>f_(p), then save this codebook vector, set        f_(p)=f(ê_(p) ⁻) and continue to next iteration.-   5. Define the codebook vector ê_(p) to be the last (that is, best)    of the saved codebook vectors.

6. If the number of pulses p has reached the desired number of pulses,then define the output vector as ê=ê_(p), and stop. Otherwise, continuewith step 4.

As already pointed out, compared to conventional ACELP applications, insome embodiments, the target is modified such that it includes the ZIRinto the following frame.

Equation 1 describes the linear predictive model used in ACELP-typecodecs. The Zero Impulse Response (ZIR, also sometimes known as the ZeroInput Response), refers to the output of the linear predictive modelwhen the residual of the current frame (and all future frames) is set tozero. The ZIR can be readily calculated by defining the residual whichis zero from position N forward as

$\begin{matrix}{\mspace{79mu} {\text{?} = \left\{ {\begin{matrix}\text{?} & {{{for}\mspace{14mu} n} < K} \\0 & {{{for}\mspace{14mu} n} \geq K}\end{matrix}\text{?}\text{indicates text missing or illegible when filed}} \right.}} & \left( {10a} \right)\end{matrix}$

whereby the ZIR can be defined as

$\begin{matrix}{\mspace{79mu} {{{ZIR}_{E}(n)} = {\sum\limits_{k = 0}^{N}\; {{h(k)}\text{?}{\left( {n - k} \right).\text{?}}\text{indicates text missing or illegible when filed}}}}} & \left( {10b} \right)\end{matrix}$

By subtracting this ZIR from the input signal, a signal is obtainedwhich depends on the residual only from the current frame forward.

Equivalently, the ZIR can be determined by filtering the past inputsignal as

$\begin{matrix}{{{ZIR}_{E}(n)} = \left\{ {\begin{matrix}{x(n)} & {{{for}\mspace{14mu} n} < K} \\{- {\sum\limits_{k = 1}^{m}\; {{a(k)}{{ZIR}_{E}\left( {n - k} \right)}}}} & {{{for}\mspace{14mu} n} \geq K}\end{matrix}.} \right.} & \left( {10c} \right)\end{matrix}$

The input signal where the ZIR has been removed is often known as thetarget and can be defined for the frame that begins at position K asd(n)=x(n)−ZIR_(K)(n). This target is in principle exactly equal to thetarget in the AMR and G.718 standards. When quantizing the signal, thequantized signal {circumflex over (d)}(n), is compared to d(n) for theduration of a frame K≤n<K+N.

Conversely, the residual of the current frame has an influence on thefollowing frames, whereby it is useful to consider its influence whenquantizing the signal, that is, one thus may want to evaluate thedifference {circumflex over (d)}(n)−d(n) also beyond the current frame,n>K+N. However, to do that, one may want to consider the influence ofthe residual of the current frame only by setting residuals of thefollowing frames to zero. Therefore, the ZIR of d(n) into the next framemay be compared. In other words, the modified target is obtained:

$\begin{matrix}{\mspace{79mu} {\text{?} = \left\{ {{\begin{matrix}0 & {n < K} \\{d(n)} & {K \leq n < {K + N}} \\\text{?} & {n > {K + N}}\end{matrix}.\text{?}}\text{indicates text missing or illegible when filed}} \right.}} & \left( {10d} \right)\end{matrix}$

Equivalently, using the impulse response h(n) of A(z), then

$\begin{matrix}{\mspace{79mu} {\text{?} = {{\text{?}.\text{?}}\text{indicates text missing or illegible when filed}}}} & \left( {10e} \right)\end{matrix}$

This formula can be written in a convenient matrix form by d′=He where Hand e are defined as in Equation 2. It can be seen that the modifiedtarget is exactly x of Equation 2.

In calculation of matrix R, note that in theory, the impulse responseh(k) is an infinite sequence, which is not realisable in a practicalsystem.

However, either

-   1) truncating or windowing the impulse response to a finite length    and determining the autocorrelation of the truncated impulse    response, or-   2) calculating the power spectrum of the impulse response using the    Fourier spectra of the associated LP and perceptual filters, and    obtain the autocorrelation by an inverse Fourier transform    is possible.

Now, an extension employing LTP is described.

The long-time predictor (LTP) is actually also a linear predictor.

According to an embodiment, the matrix determiner 110 may be configuredto determine the autocorrelation matrix R depending on a perceptuallyweighted linear predictor, for example, depending on the long-timepredictor.

The LP and LTP can be convolved into one joint predictor, which includesboth the spectral envelope shape as well as the harmonic structure. Theimpulse response of such a predictor will be very long, whereby it iseven more difficult to handle with conventional technology. However, ifthe autocorrelation of the linear predictor is already known, then theautocorrelation of the joint predictor can be calculated by simplyfiltering the autocorrelation with the LTP forward and backward, or witha similar process in the frequency domain.

Note that prior methods employing LTP have a problem when the LTP lag isshorter than the frame length, since the LTP would cause a feedback loopwithin the frame. The benefit of including the LTP in the objectivefunction is that when the lag of the LTP is shorter than frame length,then this feedback is explicitly taken into account in the optimisation.

In the following, an extension for fast optimisation in an uncorrelateddomain is described.

A central challenge in design of ACELP systems has been reduction ofcomputational complexity. ACELP systems are complex because filtering byLP causes complicated correlations between the residual samples, whichare described by the matrix B or in the current context by matrix R.Since the samples of e(n) are correlated, it is not possible to justquantise e(n) with desired accuracy, but many combinations of differentquantisations with a trial-and-error approach have to be tried, to findthe best quantisation with respect to the objective function of Equation3 or 10, respectively.

By the introduction of the matrix R, a new perspective to thesecorrelations is obtained. Namely, since R has Hermitian Toeplitzstructure, several efficient matrix decompositions can be applied, suchas the singular value decomposition, Cholesky decomposition orVandermonde decomposition of Hankel matrices (Hankel matrices areupside-down Toeplitz matrices, whereby the same decompositions can beapplied to Toeplitz and Hankel matrices) (see [6] and [7]). Let R=E DE^(H) be a decomposition of R such that D is a diagonal matrix of thesame size and rank as R. Equation 9 can then be modified as follows:

ϵ²=(e−ê)^(H) R(e−ê)=(e−ê)^(H) EDE ^(H)(e−ê)=(f−{circumflex over(f)})D(f−{circumflex over (f)})  (11)

where {circumflex over (f)}=E^(H)ê. Since D is diagonal, the error foreach sample of f(k) is independent of other samples f(i). In Equation10, it is assumed that the codebook vector is scaled by the optimalgain, whereby the new objective function is

$\begin{matrix}{\frac{\left( {f^{H}D\hat{f}} \right)^{2}}{{\hat{f}}^{H}D\hat{f}}.} & (12)\end{matrix}$

Here, the samples are again correlated (since changing the quantizationof one line changes the optimal gain for all lines), but in comparisonto Equation 10, the effect of correlation is here limited. However, evenif the correlation is taken into account, optimisation of this objectivefunction is much simpler than optimisation of Equations 3 or 10.

Using this decomposition approach, it is possible

-   1. to apply any conventional scalar or vector quantization technique    with desired accuracy, or-   2. to use Equation 12 as the objective function with any    conventional ACELP pulse search algorithm.

Both approaches give a near-optimal quantization with respect toEquation 12. Since conventional quantization techniques generally do notrequire any brute-force methods (for the exception of a possiblerate-loop), and because the matrix D is simpler than either B or R, bothquantization methods are less complex than conventional ACELP pulsesearch algorithms.

The main source of computational complexity in this approach is thus thecomputation of the matrix decomposition.

Some embodiments employ equation 12 to determine a codebook vector ofthe codebook.

E.g., several matrix factorizations for R of the form R=E^(H)DE exist.For example,

-   (a) The eigenvalue decomposition can be calculated for example by    using the GNU Scientific Library    (http://www.gnu.org/software/gsl/manual/html_node/Real-Symmetric-Matrices.html).    The matrix R is real and symmetric (as well as Toeplitz), whereby    the function “gsl_eigen_symm( )” can be used to determine the    matrices E and D. Other implementations of the same eigenvalue    decomposition are readily available in literature [6].-   (b) The Vandermonde factorization of Toeplitz matrices [7] can be    used using the algorithm described in [8]. This algorithm returns    matrices E and D such that E is a Vandermonde matrix, which is    equivalent to a discrete Fourier transform with non-uniform    frequency distribution.    -   Using such factorizations, the residual vector e can be        transformed to the transform domain by f=E^(H)e or        f′=D^(1/2)E^(H)e. Any common quantization method can be applied        in this domains, for example,-   1. The vector f′ can be quantized by an algebraic codebook exactly    as in common implementations of ACELP. However, since the elements    of f′ are uncorrelated, a complicated search function as in ACELP is    not needed, but a simple algorithm can be applied, such as    -   (a) Set initial gain to g=1    -   (b) Quantize f′ by {circumflex over (f)}′=round(gf′).    -   (c) If the number of pulses in f′ is larger than a pre-defined        amount p, ∥{circumflex over (f)}′∥₁>p, then increase gain g and        return to step b.    -   (d) Otherwise, if the number of pulses in {circumflex over (f)}′        is smaller than a pre-defined amount p, ∥{circumflex over        (f)}′∥₁>p, then decrease gain g and return to step b.    -   (e) Otherwise, the number of pulses in {circumflex over (f)}′ is        equal to the pre-defined amount p, ∥{circumflex over (f)}′∥₁>p,        and processing can be stopped.-   2. An arithmetic coder can be used similar to that used in    quantization of spectral lines in TCX in the standards AMR-WB+ or    MPEG USAC.

It should be noted that since the elements of f′ are orthogonal (as canbe seen from Equation 12) and they have the same weight in the objectivefunction of Equation 12, they can be quantized separately, and with thesame quantization step size. That quantization will automatically findthe optimal (the largest) value of the objective function in Equation12, which is possible with that quantization accuracy. In other words,the quantization algorithms presented above, will both return theoptimal quantization with respect to Equation 12.

This advantage of optimality is tied to the fact that the elements of f′can be treated separately. If a codebook approach would be used, wherethe codebook vectors are non-trivial (have more than one non-zeroelements), then these codebook vectors would not have independentelements anymore and the advantage of the matrix factorization is lost.

Observe that the Vandermonde factorization of a Toeplitz matrix can bechosen such that the Vandermonde matrix is a Fourier transform matrixbut with unevenly distributed frequencies. In other words, theVandermonde matrix corresponds to a frequency-warped Fourier transform.It follows that in this case the vector f corresponds to a frequencydomain representation of the residual signal on a warped frequency scale(see the “root-exchange property” in [8]).

Importantly, notice that this consequence is not well-known. Inpractice, this result states that if a signal x is filtered with aconvolution matrix C, then

∥Cx∥ ² =∥DVx∥ ²  (13)

where V is a (e.g., warped) Fourier transform (which is a Vandermondematrix with elements on the unit circle) and D a diagonal matrix. Thatis, if it is desired to measure the energy of a filtered signal, theenergy of frequency-warped signal can equivalently be measured. Inconverse, any evaluation that shall be done in a warped Fourier domain,can equivalently be done in a filtered time-domain. Due to the dualityof time and frequency, an equivalence between time-domain windowing andtime-warping also exists. A practical issue is, however, that finding aconvolution matrix C which satisfies the above relationship is anumerically sensitive problem, whereby often it is easier to findapproximate solutions Ĉ instead.

The relation ∥Cx∥²=∥DVx∥² can be employed for determining a codebookvector of a codebook.

For this, it should first be noted that here, by H, a convolution matrixlike in Equation 2 will be denoted instead of C. If, then, one wants tominimize the quantization noise e=Hx−H{circumflex over (x)}, its energycan be measured:

e ² =∥Hx−H{circumflex over (x)}∥ ² =∥H(x−{circumflex over(x)})∥²=(x−{circumflex over (x)})^(T) H ^(T) H(x−{circumflex over(x)})=(x−{circumflex over (x)})^(T) R(x−{circumflex over(x)})−(x−{circumflex over (x)})^(T) V ^(H) DV(x−{circumflex over(x)})−∥D ^(1/2) V(x−{circumflex over (x)})∥² −∥D ^(1/2) V(x−{circumflexover (x)})∥² −∥D ^(1/2)(f−{circumflex over (f)})∥² −∥f′−{circumflex over(f)}′∥ ².  (13a)

Now, an extension for frame-independence is described.

When the encoded speech signal is transmitted over imperfecttransmission lines such as radio-waves, invariably, packets of data willsometimes be lost. If frames are dependent on each other, such thatpacket N is needed to perfectly decode N−1, then the loss of packet N−1will corrupt the synthesis of both packets N−1 and N. If, on the otherhand, frames are independent, then the loss of packet N−1 will corruptthe synthesis of packet N−1 only. It is therefore important to devicemethods that are free from inter-frame dependencies.

In conventional ACELP systems, the main source of inter-frame dependencyis the LTP and to some extent also the LP. Specifically, since both areinfinite impulse response (IIR) filters, a corrupted frame will cause an“infinite” tail of corrupted samples. In practice, that tail can beseveral frames long, which is perceptually annoying.

Using the framework of the current invention, the path through whichinter-frame dependency is generated can be quantified by the ZIR fromthe current frame into the next is realized. To avoid this inter-framedependency, three modifications to the conventional ACELP need to bemade.

-   1 When calculating the ZIR from the previous frame into the current    (sub)frame, it should be calculated from the original (not    quantized) residual extended with zeros, not from the quantized    residual. In this way, the quantization errors from the previous    (sub)frame will not propagate into the current (sub)frame.-   2. When quantizing the current frame, the error in the ZIR into the    next frame between the original and quantized signals may be taken    into account. This can be done by replacing the correlation matrix B    with the autocorrelation matrix R, as explained above. This ensures    that the error in the ZIR into the next frame is minimised together    with the error within the current frame.-   3. Since the error propagation is due to both the LP and the LTP,    both components may be included in the ZIR. This is in difference to    the conventional approach where the ZIR is calculated for the LP    only.

If quantization errors of previous frame when quantizing the currentframe are not taken into account, efficiency in perceptual quality ofthe output is lost. Therefore, it is possible to choose to take previouserrors into account when there is no risk of error propagation. Forexample, conventional ACELP system apply a framing where every 20 msframe is sub-divided into 4 or 5 subframes. The LTP and the residual arequantized and coded separately for each subframe, but the whole frame istransmitted as one block of data. Therefore, individual subframes cannotbe lost, but only complete frames. It follows that it is important touse frame-independent ZIRs only at frame borders, but ZIRs can be usedwith interframe dependencies between the remaining subframes.

Embodiments modify conventional ACELP algorithms by inclusion of theeffect of the impulse response of the current frame into the next frame,into the objective function of the current frame. In the objectivefunction of the optimisation problem, this modification corresponds toreplacing a correlation matrix with an autocorrelation matrix that hasHermitian Toeplitz structure. This modification has the followingbenefits:

-   1. Computational complexity and memory requirements are reduced due    to the added Hermitian Toeplitz structure of the autocorrelation    matrix.-   2. The same perceptual model will be applied on all samples, making    the design and tuning of the perceptual model simpler, and its    application more efficient and consistent.-   3. Inter-frame correlations can be avoided completely in the    quantization of the current frame, by taking into account only the    unquantized impulse response from the previous frame and the    quantized impulse response into the next frame. This improves    robustness of systems where packet-loss is expected.

FIG. 2 illustrates a decoder 220 for decoding an encoded speech signalbeing encoded by an apparatus according to the above-describedembodiment to obtain a decoded speech signal. The decoder 220 isconfigured to receive the encoded speech signal, wherein the encodedspeech signal comprises the an indication of the codebook vector, beingdetermined by an apparatus for encoding a speech signal according to oneof the above-described embodiments, for example, an index of thedetermined codebook vector. Furthermore, the decoder 220 is configuredto decode the encoded speech signal to obtain a decoded speech signaldepending on the codebook vector.

FIG. 3 illustrates a system according to an embodiment. The systemcomprises an apparatus 210 according to one of the above-describedembodiments for encoding an input speech signal to obtain an encodedspeech signal. The encoded speech signal comprises an indication of thedetermined codebook vector determined by the apparatus 210 for encodinga speech signal, e.g., it comprises an index of the codebook vector.Moreover, the system comprises a decoder 220 according to theabove-described embodiment for decoding the encoded speech signal toobtain a decoded speech signal. The decoder 220 is configured to receivethe encoded speech signal. Moreover, the decoder 220 is configured todecode the encoded speech signal to obtain a decoded speech signaldepending on the determined codebook vector.

Although some aspects have been described in the context of anapparatus, these aspects also represent a description of thecorresponding method, where a block or device corresponds to a methodstep or a feature of a method step. Analogously, aspects described inthe context of a method step also represent a description of acorresponding block or item or feature of a corresponding apparatus.

The inventive decomposed signal can be stored on a digital storagemedium or can be transmitted on a transmission medium such as a wirelesstransmission medium or a wired transmission medium such as the Internet.

Depending on certain implementation requirements, embodiments of theinvention can be implemented in hardware or in software. Theimplementation can be performed using a digital storage medium, forexample a floppy disk, a DVD, a CD, a ROM, a PROM, an EPROM, an EEPROMor a FLASH memory, having electronically readable control signals storedthereon, which cooperate (or are capable of cooperating) with aprogrammable computer system such that the respective method isperformed.

Some embodiments according to the invention comprise a non-transitorydata carrier having electronically readable control signals, which arecapable of cooperating with a programmable computer system, such thatone of the methods described herein is performed.

Generally, embodiments of the present invention can be implemented as acomputer program product with a program code, the program code beingoperative for performing one of the methods when the computer programproduct runs on a computer. The program code may for example be storedon a machine readable carrier.

Other embodiments comprise the computer program for performing one ofthe methods described herein, stored on a machine readable carrier.

In other words, an embodiment of the inventive method is, therefore, acomputer program having a program code for performing one of the methodsdescribed herein, when the computer program runs on a computer.

A further embodiment of the inventive methods is, therefore, a datacarrier (or a digital storage medium, or a computer-readable medium)comprising, recorded thereon, the computer program for performing one ofthe methods described herein.

A further embodiment of the inventive method is, therefore, a datastream or a sequence of signals representing the computer program forperforming one of the methods described herein. The data stream or thesequence of signals may for example be configured to be transferred viaa data communication connection, for example via the Internet.

A further embodiment comprises a processing means, for example acomputer, or a programmable logic device, configured to or adapted toperform one of the methods described herein.

A further embodiment comprises a computer having installed thereon thecomputer program for performing one of the methods described herein.

In some embodiments, a programmable logic device (for example a fieldprogrammable gate array) may be used to perform some or all of thefunctionalities of the methods described herein. In some embodiments, afield programmable gate array may cooperate with a microprocessor inorder to perform one of the methods described herein. Generally, themethods are advantageously performed by any hardware apparatus.

While this invention has been described in terms of several embodiments,there are alterations, permutations, and equivalents which fall withinthe scope of this invention. It should also be noted that there are manyalternative ways of implementing the methods and compositions of thepresent invention. It is therefore intended that the following appendedclaims be interpreted as including all such alterations, permutationsand equivalents as fall within the true spirit and scope of the presentinvention.

REFERENCES

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1. An apparatus for encoding a speech signal by determining a codebookvector of a speech coding algorithm, wherein the apparatus comprises: amatrix determiner for determining an autocorrelation matrix R, and acodebook vector determiner for determining the codebook vector dependingon the autocorrelation matrix R, wherein the matrix determiner isconfigured to determine the autocorrelation matrix R by determiningvector coefficients of a vector r, wherein the autocorrelation matrix Rcomprises a plurality of rows and a plurality of columns, wherein thevector r indicates one of the columns or one of the rows of theautocorrelation matrix R, whereinR(i,j)=r(|i−j|), wherein R(i, j) indicates the coefficients of theautocorrelation matrix R, wherein i is a first index indicating one of aplurality of rows of the autocorrelation matrix R, and wherein j is asecond index indicating one of the plurality of columns of theautocorrelation matrix R.
 2. The apparatus according to claim 1, whereinthe matrix determiner is configured to determine the vector coefficientsof the vector r by applying the formula:${r(k)} = {{{h(k)}*{h\left( {- k} \right)}} = {\sum\limits_{l}\; {{h(l)}{h\left( {l - k} \right)}}}}$wherein h(k) indicates a perceptually weighted impulse response of alinear predictive model, and wherein k is an index being an integer, andwherein l is an index being an integer.
 3. The apparatus according toclaim 1, wherein the matrix determiner is configured to determine theautocorrelation matrix R depending on a perceptually weighted linearpredictor.
 4. The apparatus according to claim 1, wherein the codebookvector determiner is configured to determine the codebook vector byapplying the formula${f\left( \hat{e} \right)} = \frac{\left( {d^{T}\hat{e}} \right)^{2}}{{\hat{e}}^{T}R\hat{e}}$wherein R is the autocorrelation matrix, and wherein is one of thecodebook vectors of the speech coding algorithm, and wherein is anormalized f(ê) correlation.
 5. The apparatus according to claim 4,wherein the codebook vector determiner is configured to determine thatcodebook vector ê of the speech coding algorithm which maximizes thenormalized correlation${f\left( \hat{e} \right)} = {\frac{\left( {d^{T}\hat{e}} \right)^{2}}{{\hat{e}}^{T}R\hat{e}}.}$6. The apparatus according to claim 1, wherein the codebook vectordeterminer is configured to decompose the autocorrelation matrix R byconducting a matrix decomposition.
 7. The apparatus according to claim6, wherein the codebook vector determiner is configured to conduct thematrix decomposition to determine a diagonal matrix D for determiningthe codebook vector.
 8. The apparatus according to claim 7, wherein thecodebook vector determiner is configured to determine the codebookvector by employing$\frac{\left( {f^{H}D\hat{f}} \right)^{2}}{{\hat{f}}^{H}D\hat{f}},$wherein D is the diagonal matrix, wherein f is a first vector, andwherein f is a second vector.
 9. The apparatus according to claim 7,wherein the codebook vector determiner is configured to conduct aVandermonde factorization on the autocorrelation matrix R to decomposethe autocorrelation matrix R to conduct the matrix decomposition todetermine the diagonal matrix D for determining the codebook vector. 10.The apparatus according to claim 7, wherein the codebook vectordeterminer is configured to employ the equation∥Cx∥ ² =∥DVx∥ ² to determine the codebook vector, wherein C indicates aconvolution matrix, wherein V indicates a Fourier transform, and whereinx indicates the speech signal.
 11. The apparatus according to claim 7,wherein the codebook vector determiner is configured to conduct asingular value decomposition on the autocorrelation matrix R todecompose the autocorrelation matrix R to conduct the matrixdecomposition to determine the diagonal matrix D for determining thecodebook vector.
 12. The apparatus according to claim 7, wherein thecodebook vector determiner is configured to conduct a Choleskydecomposition on the autocorrelation matrix R to decompose theautocorrelation matrix R to conduct the matrix decomposition todetermine the diagonal matrix D for determining the codebook vector. 13.The apparatus according to claim 1, wherein the codebook vectordeterminer is configured to determine the codebook vector depending on azero impulse response of the speech signal.
 14. The apparatus accordingto claim 1, wherein the apparatus is an encoder for encoding the speechsignal by employing algebraic code excited linear prediction speechcoding, and wherein the codebook vector determiner is configured todetermine the codebook vector based on the autocorrelation matrix R as acodebook vector of an algebraic codebook.
 15. A method for encoding aspeech signal by determining a codebook vector of a speech codingalgorithm, wherein the method comprises: determining an autocorrelationmatrix R, and determining the codebook vector depending on theautocorrelation matrix R, wherein determining an autocorrelation matrixR comprises determining vector coefficients of a vector r, wherein theautocorrelation matrix R comprises a plurality of rows and a pluralityof columns, wherein the vector r indicates one of the columns or one ofthe rows of the autocorrelation matrix R, whereinR(i,j)=r(|i−j|), wherein R(i, j) indicates the coefficients of theautocorrelation matrix R, wherein i is a first index indicating one of aplurality of rows of the autocorrelation matrix R, and wherein j is asecond index indicating one of the plurality of columns of theautocorrelation matrix R.
 16. A decoder for decoding an encoded speechsignal being encoded by an apparatus for encoding a speech signal bydetermining a codebook vector of a speech coding algorithm, wherein theapparatus comprises: a matrix determiner for determining anautocorrelation matrix R, and a codebook vector determiner fordetermining the codebook vector depending on the autocorrelation matrixR, wherein the matrix determiner is configured to determine theautocorrelation matrix R by determining vector coefficients of a vectorr, wherein the autocorrelation matrix R comprises a plurality of rowsand a plurality of columns, wherein the vector r indicates one of thecolumns or one of the rows of the autocorrelation matrix R, whereinR(i,j)=r(|i−j|), wherein R(i, j) indicates the coefficients of theautocorrelation matrix R, wherein i is a first index indicating one of aplurality of rows of the autocorrelation matrix R, and wherein j is asecond index indicating one of the plurality of columns of theautocorrelation matrix R to acquire a decoded speech signal.
 17. Amethod for decoding an encoded speech signal being encoded according tothe method for encoding a speech signal by determining a codebook vectorof a speech coding algorithm, wherein the method for encoding comprises:determining an autocorrelation matrix R, and determining the codebookvector depending on the autocorrelation matrix R, wherein determining anautocorrelation matrix R comprises determining vector coefficients of avector r, wherein the autocorrelation matrix R comprises a plurality ofrows and a plurality of columns, wherein the vector r indicates one ofthe columns or one of the rows of the autocorrelation matrix R, whereinR(i,j)=r(|i−j|), wherein R(i, j) indicates the coefficients of theautocorrelation matrix R, wherein i is a first index indicating one of aplurality of rows of the autocorrelation matrix R, and wherein j is asecond index indicating one of the plurality of columns of theautocorrelation matrix R to acquire a decoded speech signal.
 18. Asystem comprising: an apparatus for encoding a speech signal bydetermining a codebook vector of a speech coding algorithm, wherein theapparatus comprises: a matrix determiner for determining anautocorrelation matrix R, and a codebook vector determiner fordetermining the codebook vector depending on the autocorrelation matrixR, wherein the matrix determiner is configured to determine theautocorrelation matrix R by determining vector coefficients of a vectorr, wherein the autocorrelation matrix R comprises a plurality of rowsand a plurality of columns, wherein the vector r indicates one of thecolumns or one of the rows of the autocorrelation matrix R, whereinR(i,j)=r(|i−j|), wherein R(i, j) indicates the coefficients of theautocorrelation matrix R, wherein i is a first index indicating one of aplurality of rows of the autocorrelation matrix R, and wherein j is asecond index indicating one of the plurality of columns of theautocorrelation matrix R, for encoding an input speech signal to acquirean encoded speech signal, and a decoder for decoding an encoded speechsignal being encoded by an apparatus for encoding a speech signal bydetermining a codebook vector of a speech coding algorithm, wherein theapparatus comprises: a matrix determiner for determining anautocorrelation matrix R, and a codebook vector determiner fordetermining the codebook vector depending on the autocorrelation matrixR, wherein the matrix determiner is configured to determine theautocorrelation matrix R by determining vector coefficients of a vectorr, wherein the autocorrelation matrix R comprises a plurality of rowsand a plurality of columns, wherein the vector r indicates one of thecolumns or one of the rows of the autocorrelation matrix R, whereinR(i,j)=r(|i−j|), wherein R(i, j) indicates the coefficients of theautocorrelation matrix R, wherein i is a first index indicating one of aplurality of rows of the autocorrelation matrix R, and wherein j is asecond index indicating one of the plurality of columns of theautocorrelation matrix R to acquire a decoded speech signal, fordecoding the encoded speech signal to acquire a decoded speech signal.19. A method comprising: encoding an input speech signal according tothe method for encoding a speech signal by determining a codebook vectorof a speech coding algorithm, wherein the method for encoding comprises:determining an autocorrelation matrix R, and determining the codebookvector depending on the autocorrelation matrix R, wherein determining anautocorrelation matrix R comprises determining vector coefficients of avector r, wherein the autocorrelation matrix R comprises a plurality ofrows and a plurality of columns, wherein the vector r indicates one ofthe columns or one of the rows of the autocorrelation matrix R, whereinR(i,j)=r(|i−j|), wherein R(i, j) indicates the coefficients of theautocorrelation matrix R, wherein i is a first index indicating one of aplurality of rows of the autocorrelation matrix R, and wherein j is asecond index indicating one of the plurality of columns of theautocorrelation matrix R, to acquire an encoded speech signal, anddecoding the encoded speech signal according to the method for decodingan encoded speech signal being encoded according to the method forencoding a speech signal by determining a codebook vector of a speechcoding algorithm, wherein the method for encoding comprises: determiningan autocorrelation matrix R, and determining the codebook vectordepending on the autocorrelation matrix R, wherein determining anautocorrelation matrix R comprises determining vector coefficients of avector r, wherein the autocorrelation matrix R comprises a plurality ofrows and a plurality of columns, wherein the vector r indicates one ofthe columns or one of the rows of the autocorrelation matrix R, whereinR(i,j)=r(|i−j|), wherein R(i, j) indicates the coefficients of theautocorrelation matrix R, wherein i is a first index indicating one of aplurality of rows of the autocorrelation matrix R, and wherein j is asecond index indicating one of the plurality of columns of theautocorrelation matrix R, to acquire a decoded speech signal, to acquirea decoded speech signal.
 20. A computer program for implementing, whenbeing executed on a computer or signal processor, the method forencoding a speech signal by determining a codebook vector of a speechcoding algorithm, wherein the method comprises: determining anautocorrelation matrix R, and determining the codebook vector dependingon the autocorrelation matrix R, wherein determining an autocorrelationmatrix R comprises determining vector coefficients of a vector r,wherein the autocorrelation matrix R comprises a plurality of rows and aplurality of columns, wherein the vector r indicates one of the columnsor one of the rows of the autocorrelation matrix R, whereinR(i,j)=r(|i−j|), wherein R(i, j) indicates the coefficients of theautocorrelation matrix R, wherein i is a first index indicating one of aplurality of rows of the autocorrelation matrix R, and wherein j is asecond index indicating one of the plurality of columns of theautocorrelation matrix R.
 21. A computer program for implementing, whenbeing executed on a computer or signal processor, the method fordecoding an encoded speech signal being encoded according to the methodfor encoding a speech signal by determining a codebook vector of aspeech coding algorithm, wherein the method for encoding comprises:determining an autocorrelation matrix R, and determining the codebookvector depending on the autocorrelation matrix R, wherein determining anautocorrelation matrix R comprises determining vector coefficients of avector r, wherein the autocorrelation matrix R comprises a plurality ofrows and a plurality of columns, wherein the vector r indicates one ofthe columns or one of the rows of the autocorrelation matrix R, whereinR(i,j)=r(|i−j|), wherein R(i, j) indicates the coefficients of theautocorrelation matrix R, wherein i is a first index indicating one of aplurality of rows of the autocorrelation matrix R, and wherein j is asecond index indicating one of the plurality of columns of theautocorrelation matrix R, to acquire a decoded speech signal.
 22. Acomputer program for implementing, when being executed on a computer orsignal processor, the method comprising: encoding an input speech signalaccording to the method for encoding a speech signal by determining acodebook vector of a speech coding algorithm, wherein the method forencoding comprises: determining an autocorrelation matrix R, anddetermining the codebook vector depending on the autocorrelation matrixR, wherein determining an autocorrelation matrix R comprises determiningvector coefficients of a vector r, wherein the autocorrelation matrix Rcomprises a plurality of rows and a plurality of columns, wherein thevector r indicates one of the columns or one of the rows of theautocorrelation matrix R, whereinR(i,j)=r(|i−j|), wherein R(i, j) indicates the coefficients of theautocorrelation matrix R, wherein i is a first index indicating one of aplurality of rows of the autocorrelation matrix R, and wherein j is asecond index indicating one of the plurality of columns of theautocorrelation matrix R, to acquire an encoded speech signal, anddecoding the encoded speech signal according to the method for decodingan encoded speech signal being encoded according to the method forencoding a speech signal by determining a codebook vector of a speechcoding algorithm, wherein the method for encoding comprises: determiningan autocorrelation matrix R, and determining the codebook vectordepending on the autocorrelation matrix R, wherein determining anautocorrelation matrix R comprises determining vector coefficients of avector r, wherein the autocorrelation matrix R comprises a plurality ofrows and a plurality of columns, wherein the vector r indicates one ofthe columns or one of the rows of the autocorrelation matrix R, whereinR(i,j)=r(|i−j|), wherein R(i, j) indicates the coefficients of theautocorrelation matrix R, wherein i is a first index indicating one of aplurality of rows of the autocorrelation matrix R, and wherein j is asecond index indicating one of the plurality of columns of theautocorrelation matrix R, to acquire a decoded speech signal, to acquirea decoded speech signal.